Pro-independence Scottish MPs are increasing pressure on the UK government to set a date for a fresh Scottish independence referendum, even as new polls suggest support for the country's self-determination may be too weak.

Scotland’s First Minister Nicola Sturgeon had been insisting that a second Scottish independence vote would have to happen before the UK exits the European Union in March 2019, once the terms of the Brexit deal are clear.

On Tuesday, however, she indicated that she might consider delaying the vote until after Brexit if British Prime Minister Theresa May could come to an agreement on the referendum’s timing.

But putting off the vote may be in Sturgeon’s best interests, if the latest polls are to be believed.

A survey by ScotCen’s Scottish Social Attitudes released on Wednesday showed that Sturgeon risked defeat even though Scottish support for independence was at 46 percent, its highest level since 1999.

The survey unearthed a sticking point: Euroscepticism in Scotland is on the rise, which suggests that support for the EU may be too weak to push voters towards voting for independence, undermining Sturgeon's argument.

In a separate opinion poll by YouGov, published in The Times newspaper on Wednesday, support for independence was found to be at its lowest in two-and-a-half-years.

The poll of around 1,000 Scots, taken from March 9 to 14, found that 43 percent of respondents favoured independence while 57 percent would prefer to remain part of the UK.

Prime Minister May has rejected the idea of a second vote as "divisive".

But in an interview with the Guardian yesterday, Angus Robertson, leader of the Scottish National Party (SNP) in Britain’s parliament, said time was running out for the prime minister. He explained that where the SNP's efforts are "currently focused is trying to convince the UK government to come to a compromise agreement protecting Scotland's place in Europe".

“If the UK government genuinely believes in a United Kingdom [it must] take the needs, interests, concerns of the different parts of the UK seriously,” Robertson said.

Britain's Scotland minister David Mundell has challenged Sturgeon’s demands for a deadline, saying it would make it impossible to have a legal and decisive referendum on Scottish independence.

In an interview with Scotland’s Herald newspaper published on Wednesday, Mundell added that there was “no option for Scotland to remain in the EU as the UK leaves or for Scotland to inherit the UK’s place”.

“There’s an implicit suggestion in the timing of the referendum demand that somehow by having a referendum and by voting for independence you can stop Scotland leaving the EU; that’s absurd," he said.

Despite the intransigence of the British government, Robertson said he remained hopeful of a compromise. Should that fail, however, an independence vote would be inevitable.